Create an ANTLR$4$ grammar for an easy calculator language based on the following specifications.

program $-->$ declaration$*$ statement$*$ $$

declaration $-->$ bool identifier ; $|$ int identifier ; $|$ real identifier ;

statement $-->$ identifier :$=$ expression ; $|$ read identifier ; $|$ write expression ;

expression $-->$ expression operator expression $|$ identifier $|$ literal $|($expression $)|$ to$\_$int $($expression $)|$ to$\_$real $($expression$)|$ if expression then expression else expression

operator $-->*|\frac{?}{?}|+|-|$ and $|$ or $|<|>|==$

literal $-->$ real$\_$number $|$ int$\_$number $|$ true $|$ false

Use precedence from C language to get the precedence of the operators. An identifier starts with a letter and can contain letters, numbers, and underscores. An integer number is one or more digits. A real number contains a dot and at least one digit. A printer file ParserApp. java is provided. This file should be in the and is used to test whether your created grammar is correct or not. Here are the test cases you can use to test your results. Note that you should also check whether the parsing follows correct operator precedence.

Test $1($should NOT parse$)$

int a;

a :$=2+3$;

bool b;

$$

Test $2($should parse$)$

int a;

bool b;

a :$=2+3$;

b :$=$ false;

$$

Test $3($should parse$)$

a :$=((2+3))$;

$$

Test $4($should parse$)$

a :$=$ if true then $2$ else $4$;

$$

Test $5($should parse$)$

bool a;

int $b$;

real $c$;

$$

Test $6($should parse$)$

a :$=2+3$;

read a;

write $2+3$;

$$

Test $7($should NOT parse$)$

read $2+3$;

$$

Test $8($should parse$)$

a :$=2+3-4*\frac{5}{2}>b$ and $c>d$;

$$

import java.util.$*$;

import org.antlr.v$4.$runtime.$*$;

import org.antlr.v$4.$runtime.tree.$*$;

import easycalc.grammar.$*$;

public class ParserApp $\{$

public static void main$($String$[]$ args$)\{$

$//$ Read in multiple lines of input$//$

StringBuilder sb $=$ new StringBuilder$()$;

Scanner scan $=$ new Scanner$($System$.$in$)$;

String nextLine $=$ scan.nextLine$()$;

while $(!$nextLine.contains$("$$$$"))\{$

sb$.$append $($nextLine$)$;

scan $=$ new Scanner$($System$.$in$)$;

nextLine $=$ scan.nextLine$()$;

$\}$

scan.close$()$;

sb$.$append$($nextLine$)$;

String str $=$ sb$.$toString$()$;

$//$Create the parse tree from the input

CharStream input $=$ CharStreams.fromString$($str$)$;

EasyCalcLexer lexer $=$ new EasyCalcLexer$($input$)$;

CommonTokenStream tokens $=$ new CommonTokenStream$($lexer$)$;

EasyCalcParser parser $=$ new EasyCalcParser$($tokens$)$;

ParseTree tree $=$ parser.program$()$; $//$begin parsing at program rule

$//$Print out the LISP$-$style tree

System.out.println$($tree$.$toStringTree$($parser$))$;

$\}$

$\}$